Correct Answer - Option 3 : 16
Given:
Number of workers in team I = W
Number of workers in team II = W
New number of workers in team I = W - 1
New number of workers in team II = W + 1
Formula used:
Total work done = Number of workers × Time taken
Calculations:
Total work done by (W - 1) workers in team I = (W - 1)(W + 1)
Total work done by (W + 1) workers in team II = (W + 1)(W + 2)
According to question,
(W - 1)(W + 1)/(W + 1)(W + 2) = 10 : 12
⇒ (W2 - 1)/(W2 + 3W + 2) = 5 : 6
⇒ 6W2 - 6 = 5(W2 + 3W + 2)
⇒ 6W2 - 6 = 5W2 + 15W + 10
⇒ W2 - 15W - 16 = 0
⇒ (W - 16)(W + 1) = 0
(W - 16) = 0 or (W + 1) = 0
⇒ W = 16 or (W + 1) = 0
W ≠ -1
So, W = 16.
∴ The value of W is 16.